FTC and Particle Motion
Which of the following statements best illustrates the First Fundamental Theorem of Calculus by relating a particle’s position and velocity functions for straight-line motion?
The velocity function is the second derivative of the position function, and its integral gives the particle’s acceleration over time.
The position function is the square root of the integral of the velocity function, illustrating the theorem’s application to non-linear motion.
The velocity function is the derivative of the position function, and the definite integral of the velocity function over an interval gives the displacement of the particle.
The position function is the antiderivative of the velocity function, but the integral of the position function does not relate to the particle’s motion.
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